Контрольные задания > 177. Вычислите: 1) $$6\frac{4}{9}+3\frac{5}{9}$$; 2) $$10\frac{11}{19}+5\frac{14}{19}$$; 3) $$2\frac{3}{13}+2\frac{11}{13}$$; 4) $$1\frac{5}{8}+3\frac{7}{8}$$; 5) $$1-\frac{3}{11}$$; 6) $$1-\frac{13}{40}$$; 7) $$4-1\frac{1}{4}$$; 8) $$10-9\frac{3}{10}$$; 9) $$5\frac{2}{7}-2\frac{5}{7}$$; 10) $$14\frac{6}{20}-8\frac{12}{20}$$; 11) $$8\frac{3}{9}-5\frac{5}{9}$$; 12) $$7\frac{10}{21}-4\frac{16}{21}$$; 13) $$14\frac{8}{31}-6\frac{8}{31}$$; 14) $$(12\frac{5}{22}+7\frac{17}{22})-(13\frac{7}{23}-9\frac{15}{23})$$.
Вопрос:

177. Вычислите: 1) $$6\frac{4}{9}+3\frac{5}{9}$$; 2) $$10\frac{11}{19}+5\frac{14}{19}$$; 3) $$2\frac{3}{13}+2\frac{11}{13}$$; 4) $$1\frac{5}{8}+3\frac{7}{8}$$; 5) $$1-\frac{3}{11}$$; 6) $$1-\frac{13}{40}$$; 7) $$4-1\frac{1}{4}$$; 8) $$10-9\frac{3}{10}$$; 9) $$5\frac{2}{7}-2\frac{5}{7}$$; 10) $$14\frac{6}{20}-8\frac{12}{20}$$; 11) $$8\frac{3}{9}-5\frac{5}{9}$$; 12) $$7\frac{10}{21}-4\frac{16}{21}$$; 13) $$14\frac{8}{31}-6\frac{8}{31}$$; 14) $$(12\frac{5}{22}+7\frac{17}{22})-(13\frac{7}{23}-9\frac{15}{23})$$.

Ответ:

Вычисление выражений:

  1. $$6\frac{4}{9}+3\frac{5}{9} = (6+3) + (\frac{4}{9}+\frac{5}{9}) = 9 + \frac{9}{9} = 9 + 1 = 10$$
  2. $$10\frac{11}{19}+5\frac{14}{19} = (10+5) + (\frac{11}{19}+\frac{14}{19}) = 15 + \frac{25}{19} = 15 + 1\frac{6}{19} = 16\frac{6}{19}$$
  3. $$2\frac{3}{13}+2\frac{11}{13} = (2+2) + (\frac{3}{13}+\frac{11}{13}) = 4 + \frac{14}{13} = 4 + 1\frac{1}{13} = 5\frac{1}{13}$$
  4. $$1\frac{5}{8}+3\frac{7}{8} = (1+3) + (\frac{5}{8}+\frac{7}{8}) = 4 + \frac{12}{8} = 4 + 1\frac{4}{8} = 5\frac{1}{2}$$
  5. $$1-\frac{3}{11} = \frac{11}{11} - \frac{3}{11} = \frac{11-3}{11} = \frac{8}{11}$$
  6. $$1-\frac{13}{40} = \frac{40}{40} - \frac{13}{40} = \frac{40-13}{40} = \frac{27}{40}$$
  7. $$4-1\frac{1}{4} = 4 - \frac{5}{4} = \frac{16}{4} - \frac{5}{4} = \frac{16-5}{4} = \frac{11}{4} = 2\frac{3}{4}$$
  8. $$10-9\frac{3}{10} = 10 - \frac{93}{10} = \frac{100}{10} - \frac{93}{10} = \frac{100-93}{10} = \frac{7}{10}$$
  9. $$5\frac{2}{7}-2\frac{5}{7} = \frac{37}{7} - \frac{19}{7} = \frac{37-19}{7} = \frac{18}{7} = 2\frac{4}{7}$$
  10. $$14\frac{6}{20}-8\frac{12}{20} = 14\frac{3}{10} - 8\frac{6}{10} = \frac{143}{10} - \frac{86}{10} = \frac{57}{10} = 5\frac{7}{10}$$
  11. $$8\frac{3}{9}-5\frac{5}{9} = 8\frac{1}{3}-5\frac{5}{9} = \frac{25}{3} - \frac{50}{9} = \frac{75}{9} - \frac{50}{9} = \frac{25}{9} = 2\frac{7}{9}$$
  12. $$7\frac{10}{21}-4\frac{16}{21} = 7\frac{10}{21} - 4\frac{16}{21} = \frac{157}{21} - \frac{100}{21} = \frac{57}{21} = \frac{19}{7} = 2\frac{5}{7}$$
  13. $$14\frac{8}{31}-6\frac{8}{31} = \frac{442}{31} - \frac{194}{31} = \frac{248}{31} = 8$$
  14. $$(12\frac{5}{22}+7\frac{17}{22})-(13\frac{7}{23}-9\frac{15}{23}) = ((12+7)+(\frac{5}{22}+\frac{17}{22}))-((13-9)+(\frac{7}{23}-\frac{15}{23})) = (19+\frac{22}{22})-(4+\frac{-8}{23}) = (19+1)-(4-\frac{8}{23}) = 20-(4-\frac{8}{23}) = 20-4+\frac{8}{23} = 16+\frac{8}{23} = 16\frac{8}{23}$$
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